A milkman has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk. If the cost of pure milk is Rs. 18 per litre, then the profit of the milkman, when he sells all the mixture at cost price, is:

(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.

Total distance to be covered = (360 + 140) m = 500 m.

Let the length of the train be x metres and its speed by y m/sec.

∴ 9y - 5 = x and 10(9y - 10) = 9x

⟹ 9y - x = 5 and 90y - 9x = 100.

On solving, we get: x = 50.

∴ Length of the train is 50 m.

∴   x = 3, as 632 is divisible 8.

So, the required number must be divisible by each one of 3, 7, 47

553681 → (Sum of digits = 28, not divisible by 3)

555181 → (Sum of digits = 25, not divisible by 3)

555681 is divisible by 3, 7, 47.

On dividing 2497 by 60, the remainder is 37.

∴ Number to be added = (60 - 37) = 23.

Then, (17)^{3.5 + x} = 17⁸.

∴ 3.5 + x = 8

⟹ x = (8 - 3.5)

⟹ x = 4.5

A leap year has (52 week + 2 days).
So, the number of odd days in a leap year is 2

Series pattern
16 x 0.25 = 4,
4 x 0.50 = 2,
2 x 0.75 =1.5,
1.5 x 1.00 = 1.5
Should come in place of 1.75
1.5 x 1.25 = 1.875
Clearly, 1.75 is wrong and will be replaced by 1.5

The ratio of speeds = The ratio of distances, when time is constant
? The ratio of distance covered by leopard to the tiger = 12 : 25
Again, ratio of rounds made by leopard to the tiger = 12 : 25
hence, leopard makes 48 rounds, when tiger makes 100 rounds